In order to evaluate the conformal Einstein constraints on
\(\mathcal {H}\) , we first consider the equations (REF )-() on
timelike hypersurfaces for which the conformal factor \(\Omega \)  is
constant. On these hypersurfaces one has, in adapted coordinates,
that \(D_i\zeta =0\)  and \(D_i D_j\zeta =0\) . Following the discussion in
[1]} define
\(\digamma \equiv N^a \nabla _a \Omega .\) 
